Question: A circle has a circumference of ${6}$. It has an arc of length $\dfrac{17}{3}$. What is the central angle of the arc, in degrees?
Solution: The ratio between the arc's central angle $\theta$ and $360^\circ$ is equal to the ratio between the arc length $s$ and the circle's circumference $c$. $\dfrac{{\theta}}{360^\circ} = \dfrac{{s}}{{c}}$ $\dfrac{{\theta}}{360^\circ} = {\dfrac{17}{3}} \div {6}$ $\dfrac{{\theta}}{360^\circ} = \dfrac{17}{18}$ ${\theta} = \dfrac{17}{18} \times 360^\circ$ ${\theta} = 340^\circ$ ${6}$ ${\dfrac{17}{3}}$ ${340^\circ}$